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Asymptotic Geometry of Teichmuller Space: Thickness and Divergence

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Harold Sultan (Columbia)

Abstract:
I will talk about the asymptotic geometry of Teichmuller
space equipped with the Weil-Petersson metric. In particular, I will
give a criterion for determining when two points in the asymptotic
cone of Teichmuller space can be separated by a point; motivated by a
similar characterization in mapping class groups by
Behrstock-Kleiner-Minsky-Mosher and in right angled Artin groups by
Behrstock-Charney. I will also explain two new ways to uniquely
characterize the Teichmuller space of the genus two once punctured
surface amongst all Teichmuller spaces: one is that it is thick of
order two and the other is that it has a divergence function which is
superquadratic yet subexponential.